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Knowing whether poverty rates converge within a country matters for regional development policy and for understanding growth processes. In this paper, we use five poverty measures, calculated biennially from 2004 to 2014 for 100 districts in Pakistan, to test for poverty convergence. Spatial autoregressive models are used to capture spatial spillovers. Conventional money‐metric poverty measures, such as the headcount index and poverty gap index, show unconditional convergence, and the convergence is more apparent if indirect impacts from spillovers are accounted for. In contrast, two multidimensional poverty indices show no convergence and no indirect impacts from spatial spillovers. Catch‐up growth in initially poorer areas is apparent with the money‐metric poverty measures traditionally used in Pakistan but not with the types of multidimensional poverty measures used officially since 2015. This difference in apparent poverty convergence could affect regional development policy choices. [ABSTRACT FROM AUTHOR]